Make the shortcakes: Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper. Whisk the heavy cream, sour cream and vanilla in a small bowl; refrigerate until ready to use. Pulse the flour, granulated sugar, baking powder and salt in a food processor until combined. Add the butter; pulse until the mixture looks like fine meal. Transfer to a large bowl and stir in the chocolate chips and 1 cup shredded coconut. Gently fold in the heavy cream mixture using a rubber spatula until just combined.
Divide the dough into 6 pieces on the prepared baking sheet; pat into 3-inch rounds (about 1 inch high). Brush the rounds with heavy cream and sprinkle with the remaining 1/2 cup shredded coconut. Bake until lightly browned and slightly firm to the touch, about 30 minutes. Let cool on the baking sheet.
Meanwhile, make the toppings: Toss the strawberries, 1/4 cup brown sugar and the vanilla in a medium bowl; set aside.
Just before serving, beat the heavy cream, sour cream and the remaining 1/4 cup brown sugar in a large bowl with a mixer on medium-high speed until soft peaks form, about 2 minutes. Split the shortcakes in half; sandwich the strawberries and cream between the halves.